A theory for self-fields effects on dispersion relation in a free-electron laser with planar wiggler and ion-channel guiding
is presented. An equation is derived for dispersion relation in the presence of the electromagnetic radiation, space-charge
wave, ion-channel electrostatic field, and self-fields. Numerical solution of this equation is used to study growth rate. A
comparison between the growth rates in the presence and absence of self-fields shows that the growth rate decreases
considerably due to the self-fields.